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Problem 13 Medium Difficulty

Find the solution of the differential equation that satisfies the given initial condition.
$ \frac {du}{dt} = \frac {2t + \sec^2t}{2u}, u(0) = 0 $

Answer

$u=-\sqrt{t^{2}+\tan t+25}$

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MS

Matt S.

October 23, 2021

Why no plus/minus?

Video Transcript

this question asked us to find the solution of the differential equation that satisfies the given additional condition. We know we have d'you over G is two teeth plus sequence where team divide by to you. Now let's get all the you terms on left inside to you D you and all the ti terms on the right hand side because it will make it significantly easier to integrate. Take the integral of both sides. Tiu to you becomes you squared because we increase the exploited by one and we divide by the new exponents. Marco, fishing just becomes one or two over too. On the right hand side, we have cheese squared plus tan of team plus c Remember, the integral seeking scored of tea is 10 of tea. Now that we have this, we know we're gonna be substituting. And if you have zero is negative five than t zero and use negative five substitute in. Remember, we're solving for C. We got C is 25. Lastly, plug back in to our equation that we determined once we integrated the sea is 25 instead of plus C, we now have plus 25 then take the squirt of both sides. Because we want this in terms of singular. You not. You squared and we end up with our solution. So this is all under the square root now?